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Chapter 2 · Fractions · page 12 of 68

Mixed numbers and improper fractions

levelGrade 5
standard5.NF
practiceFraction operations

A mixed number is a whole plus a fraction, like 1½. An improper fraction has a top bigger than its bottom, like 3/2. They are the same number written two ways. Improper is easier to calculate with. Mixed is easier to picture.

How to use it

  1. Mixed to improper: multiply the whole by the bottom, add the top, keep the bottom.
  2. Improper to mixed: divide top by bottom. The quotient is the whole, the remainder is the new top.
  3. To add mixed numbers, either convert both to improper, or add wholes and fractions separately and carry.

Example

112=2⋅1+12=321\tfrac{1}{2} = \frac{2 \cdot 1 + 1}{2} = \frac{3}{2}
74=134\frac{7}{4} = 1\tfrac{3}{4}
212+134=3+54=4142\tfrac{1}{2} + 1\tfrac{3}{4} = 3 + \frac{5}{4} = 4\tfrac{1}{4}

Where it goes wrong

  • Reading 1½ as 1 × ½. The space means plus.
  • Forgetting to carry when the fraction part reaches a whole.

Related

Adding and subtracting fractionsWhat a fraction is
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